It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have ans...It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].展开更多
In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, t...In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, the authors obtain the weightd inequalies for a wide class of sublinear singular operators defined onR n which include the Calderón-Zygmund operators as special cases. The fractional versions of these results are also given.展开更多
Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they ar...Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.展开更多
The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators Mn. We derive the complete asymptotic expansion of the operators Mn and their derivatives as n tends to infinit...The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators Mn. We derive the complete asymptotic expansion of the operators Mn and their derivatives as n tends to infinity. It turns out that the appropriate representation is a series of reciprocal factorials. All coefficients are calculated explicitly in a very concise form. Our main theorem contains several earlier partial results as special cases. Finally, we obtain a Voronovskaja-type formula for simultaneous approximation by linear combinations of Mn,展开更多
This paper deals with Kolmogorov criterion for best uniform coapproximation and strongly unique best uniform coapproximation. Some relations between best uniform approximation and best uniform coapproximation are obta...This paper deals with Kolmogorov criterion for best uniform coapproximation and strongly unique best uniform coapproximation. Some relations between best uniform approximation and best uniform coapproximation are obtained. Some equalities and best uniform coapproximation are connected.展开更多
In this paper, we establish two multiplier theorems for Herz type Hardy spaces, and as an application, we discuss the boundedness of pseudo-differential operators in these spaces.
In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P...In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P（x,y） is a nontrivial and real-valued polynomial defined on R^n×R^n,Ω（x） is homogeneous of degree zero on R^n, As（x） has derivatives of order ms in ∧βs （0〈βs〈 1）, Rms＋1 （As;x, y） denotes the （ms＋1）-st remainder of the Taylor series of As at x expended about y （s = 1, 2, ..., r）, M = ∑s^r =1 ms, the author proves that if 0 〈=β1=∑s^r=1 βs〈1,and Ω∈L^q（S^n-1） for some q 〉 1/（1 -β）, then for any p∈（1, ∞）, and some appropriate 0 〈β〈 1, TA1,A2,...,Ar, is bounded on L^P（R^n）.展开更多
In this note a new generalized version of the classical Landau-Kolmogorov and Stein inequalities is established on a convolution class of periodic functions with a NCVD kernel. On this basis some sets of optimal subsp...In this note a new generalized version of the classical Landau-Kolmogorov and Stein inequalities is established on a convolution class of periodic functions with a NCVD kernel. On this basis some sets of optimal subspaces for the 2n-dimensional Kolgmogorov width of such function class are identified.展开更多
The commutators of oscillatory singular integral operators with homogeneous kernel $\frac{{\Omega (x)}}{{\left| x \right|^n }}$ are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphe...The commutators of oscillatory singular integral operators with homogeneous kernel $\frac{{\Omega (x)}}{{\left| x \right|^n }}$ are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphere. It is proved that Ω∈L (logL)K+1(Sn-1) is a sufficient condition under which the k-th order commutator is bounded on L2(Rn).展开更多
In this paper we present a general conclusion of looking for the exact value of Hausdorff measure of Sierpinski carpet and construct a special partial cover of the carpet. And then we obtained an upper bound of the va...In this paper we present a general conclusion of looking for the exact value of Hausdorff measure of Sierpinski carpet and construct a special partial cover of the carpet. And then we obtained an upper bound of the value, which is the least one as we know. A conjecture for the measure is proposed at last.展开更多
In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for gener...In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.展开更多
We consider the oscillatory integral operator Ta,mf（X） f（y）dy, where the function f is a Schwartz function.In this paper, the restriction theorem on Sn-1 for this operator is obtained. Moreover, we obtain a necess...We consider the oscillatory integral operator Ta,mf（X） f（y）dy, where the function f is a Schwartz function.In this paper, the restriction theorem on Sn-1 for this operator is obtained. Moreover, we obtain a necessary condition which ensures validity of the restriction theorem.展开更多
In this paper, we systematically study a class of waves. We then de fine Hardy type spaces by conjugate systems for this class of waves, and study their properties. In particular, we show that they extend some class o...In this paper, we systematically study a class of waves. We then de fine Hardy type spaces by conjugate systems for this class of waves, and study their properties. In particular, we show that they extend some class of Lp estimates for the wave equation.展开更多
This is a short survey on osicllatory integral operators. We summarize the main development and managing techniques of the field, and give some open problems and main references in the end.
文摘It is shown that the Stein-Weiss conjugate harmonic function is the Quarternion and the Octonion analytic function. We find a counter example to show the converse is not ture in the Octonion case, by which we have answered the question proposed in [1].
文摘In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, the authors obtain the weightd inequalies for a wide class of sublinear singular operators defined onR n which include the Calderón-Zygmund operators as special cases. The fractional versions of these results are also given.
文摘Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.
文摘The concern of this paper is to study local approximation properties of the Bernstein-Durrmeyer operators Mn. We derive the complete asymptotic expansion of the operators Mn and their derivatives as n tends to infinity. It turns out that the appropriate representation is a series of reciprocal factorials. All coefficients are calculated explicitly in a very concise form. Our main theorem contains several earlier partial results as special cases. Finally, we obtain a Voronovskaja-type formula for simultaneous approximation by linear combinations of Mn,
文摘This paper deals with Kolmogorov criterion for best uniform coapproximation and strongly unique best uniform coapproximation. Some relations between best uniform approximation and best uniform coapproximation are obtained. Some equalities and best uniform coapproximation are connected.
文摘In this paper, we establish two multiplier theorems for Herz type Hardy spaces, and as an application, we discuss the boundedness of pseudo-differential operators in these spaces.
文摘In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P（x,y） is a nontrivial and real-valued polynomial defined on R^n×R^n,Ω（x） is homogeneous of degree zero on R^n, As（x） has derivatives of order ms in ∧βs （0〈βs〈 1）, Rms＋1 （As;x, y） denotes the （ms＋1）-st remainder of the Taylor series of As at x expended about y （s = 1, 2, ..., r）, M = ∑s^r =1 ms, the author proves that if 0 〈=β1=∑s^r=1 βs〈1,and Ω∈L^q（S^n-1） for some q 〉 1/（1 -β）, then for any p∈（1, ∞）, and some appropriate 0 〈β〈 1, TA1,A2,...,Ar, is bounded on L^P（R^n）.
文摘In this note a new generalized version of the classical Landau-Kolmogorov and Stein inequalities is established on a convolution class of periodic functions with a NCVD kernel. On this basis some sets of optimal subspaces for the 2n-dimensional Kolgmogorov width of such function class are identified.
文摘The commutators of oscillatory singular integral operators with homogeneous kernel $\frac{{\Omega (x)}}{{\left| x \right|^n }}$ are studied, where Ω is homogeneous of degree zero, has mean value zero on the unit sphere. It is proved that Ω∈L (logL)K+1(Sn-1) is a sufficient condition under which the k-th order commutator is bounded on L2(Rn).
文摘In this paper we present a general conclusion of looking for the exact value of Hausdorff measure of Sierpinski carpet and construct a special partial cover of the carpet. And then we obtained an upper bound of the value, which is the least one as we know. A conjecture for the measure is proposed at last.
文摘In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.
文摘We consider the oscillatory integral operator Ta,mf（X） f（y）dy, where the function f is a Schwartz function.In this paper, the restriction theorem on Sn-1 for this operator is obtained. Moreover, we obtain a necessary condition which ensures validity of the restriction theorem.
文摘In this paper, we systematically study a class of waves. We then de fine Hardy type spaces by conjugate systems for this class of waves, and study their properties. In particular, we show that they extend some class of Lp estimates for the wave equation.
文摘This is a short survey on osicllatory integral operators. We summarize the main development and managing techniques of the field, and give some open problems and main references in the end.
